1. Elliptic Flow and Constituent Quark Scaling
Marcus Bleicher1 & Xianglei Zhu2
1Institut für Theoretische Physik
2Frankfurt Institute for Advanced Studies
Goethe Universität Frankfurt
Germany
Marcus Bleicher, Strange Quark Matter 2006

2. Thanks to the UrQMD group @ Frankfurt
Sascha Vogel (Resonances)
Stephane Haussler (Event-by-Event Fluctuations)
Hannah Petersen (Flow at FAIR)
Diana Schumacher (Di-Leptons)
Qingfeng Li (HBT)
Xianglei Zhu (Elliptic Flow and Charm)
and Horst Stoecker, Yan Lu, Paul Sorensen, Nu Xu
Marcus Bleicher, Strange Quark Matter 2006

3. Parton Number Scaling of v2
in leading order of v2, recombination predicts:
Is this the only explanation?
P. Soerensen, UCLA & SQM2003
Bass, Nonaka, Mueller, Fries, 2003
Marcus Bleicher, Strange Quark Matter 2006

4. Contents Introduction Different methods for v2
Constituent quark scaling
Summary
Marcus Bleicher, Strange Quark Matter 2006

5. The tool: UrQMDv2.2 Non-equilibrium transport model
Hadrons and resonances
String excitation and fragmentation
Cross sections are parameterized
via AQM or calculated by detailed balance
pQCD hard scattering at high energies
Generates full space-time dynamics of hadrons and strings
Marcus Bleicher, Strange Quark Matter 2006

6. Model check: Multiplicities
Rapidity distributions in line with data (Phobos)
Centrality dependence in line with data
Marcus Bleicher, Strange Quark Matter 2006

7. Model check: pp-correlations
Q. Li, M.B., H. Stoecker, nucl-th/ ; Data: STAR
Correlations are well described except for most central reactions
Marcus Bleicher, Strange Quark Matter 2006

8. Anisotropic flow v1 – directed flow v2 -- elliptic flow
Fourier expansion of the transverse
angular distribution of the emitted particles:
Reaction Plane
v1 – directed flow
v2 -- elliptic flow
Marcus Bleicher, Strange Quark Matter 2006

9. coordinate-space-anisotropy  momentum-space-anisotropy
Elliptic flow
coordinate-space-anisotropy  momentum-space-anisotropy y py x px
Elliptic flow is a self-quenching effect  shuts itself off after the early stage of the reaction
Radial flow (<pT>) is an integral quantity  developed over the whole reaction time
Marcus Bleicher, Strange Quark Matter 2006

10. Are these unique QGP signatures?
V2 at RHIC
Magnitude of v2 is large
Meson-baryon ordering
Constituent quark scaling
Decrease of v2 at high pT
Are these unique QGP signatures?
Marcus Bleicher, Strange Quark Matter 2006

11. Cumulant: Rapidity Differential flow
At large eta, the non-flow effects are less obvious. If the v2 fluctuations are also negligible to the cumulant method, the v2{2}, v2{4} and v2{6} should all agree with the exact v2.
X. Zhu, M.B., H. Stoecker, Phys.Rev.C72:064911,2005
Marcus Bleicher, Strange Quark Matter 2006

12. Cumulants: Centrality
Integral flow
In the most central bin:
The fluctuations give larger v2{6} but smaller v2{4}
In the very peripheral bins:
The fluctuations give larger v2{6} and v2{4}
Agree with the prediction of MCG model
BUT:
In the semi-central bins:
the v2 fluctuations can be neglected.
X. Zhu, M.B., H. Stoecker, Phys.Rev.C72:064911,2005
Marcus Bleicher, Strange Quark Matter 2006

13. Compare apples to apples
Differential flow
v2{2} is heavily affected by the non-flow effects especially at large pT.
The non-flow effects have been eliminated in v2{4} and v2{6}.
But v2{4} is still a little larger than the exact v2.  Use Lee-Yang zero method
X. Zhu, M.B., H. Stoecker, Phys.Rev.C72:064911,2005
LYZ-method in UrQMD: nucl-th/
Marcus Bleicher, Strange Quark Matter 2006

14. Elliptic flow: Magnitude
Integral flow
V2 from UrQMD is about 50% smaller than the data
Space for parton rescattering?
STAR data is from
nucl-ex/
X. Zhu, M.B., H. Stoecker, Phys.Rev.C72:064911,2005
Marcus Bleicher, Strange Quark Matter 2006

15. Energy dependence Qualitative description OK
Importance of potentials at low energies
Lack of pressure shows up at lower SPS energies
H. Petersen, X. Zhu, M.B.
Marcus Bleicher, Strange Quark Matter 2006

16. When is v2 created?
The earlier a particle is emitted the larger is the elliptic flow
The higher the pT of a particle the larger is the elliptic flow
High pT particles are more sensitive to the initial v2
Y. Lu, M.B., et al., nucl-th/
Marcus Bleicher, Strange Quark Matter 2006

17. Initial ‘string matter’
String matter dominates the early stages
lack of early pressure
‘string matter‘ = QGP?
Strong color field or color glas or a hydrodynamical initial state fix the initial pressure problem
H. Petersen, X. Zhu, M.B.
Marcus Bleicher, Strange Quark Matter 2006

18. Back to the story line:
Messengers from the mixed phase: Multi-strange hadrons
freeze-out early
all v2 should be from QGP
Thus, if W, X and f have sufficient v2
Proof of partonic collectivity (maybe QGP)
Marcus Bleicher, Strange Quark Matter 2006

19. Indications of early freeze-out
Two different groups: (a) p,K,p (b) f, W
Multi-strange particle freeze-out earlier than bulk
K. Schweda, STAR
Where will be the charm?
 Sensitivity to early (partonic) stage
Marcus Bleicher, Strange Quark Matter 2006

20. Early freeze-out: models
Flow ordering
 different hadronic cross sections
UrQMD, RHIC
A. Dumitru, S. Bass, M.B., H. Stoecker, Phys.Lett.B460: ,1999
Marcus Bleicher, Strange Quark Matter 2006

21. Do multi-strange hadrons flow?
Data indicates approximate 3:2 scaling with constituent quarks
Baryons are generally below mesons
Decrease of v2 at high pT Is this rough scaling a signal for recombination?
P. Sorensen, SQM 2006
Marcus Bleicher, Strange Quark Matter 2006

22. V2(pT) for various hadrons
min. bias
Maybe its just the additive Quark model?
UrQMD
Y. Lu, M.B., et al., nucl-th/
Open – Mesons Full -- Baryons
1) Clear separation of meson and baryon v2
2) Low pT, v2(meson)>v2(baryon)
3) High pT, v2(m)<v2(b)
4) v2’s of multi-strange hadrons comparable to light hadrons
Marcus Bleicher, Strange Quark Matter 2006

23. NCQ-scaling NCQ-scaling of v2 is roughly reproduced in UrQMD!
there might be an ordering of v2/n: W<X<L<N
UrQMD
Y. Lu, M.B., et al., nucl-th/
AQM cross sections:
Np: 26 mb Lp: 23 mb Xp: 20 mb Wp: 16 mb
pp: 18 mb Kp: 14 mb
NCQ-scaling of v2 is roughly reproduced in UrQMD!
Marcus Bleicher, Strange Quark Matter 2006

24. B-M Asymmetry
Inclusion of gluons in recombination was predicted to lead to a larger meson v2/n than baryon v2/n:
B.Müller, et al. nucl-th/
Marcus Bleicher, Strange Quark Matter 2006

25. Summary At RHIC (transport models w/ strings and hadrons):
Part of v2 might also come from hadronic stage
non-flow correlations are correct
Mass ordering is correct
(B-M) Asymmetry has correct shape
Constituent quark scaling (w/o ReCo! but AQM)
However, transport models w/o QGP produce too few pressure in the early stage above 30 GeV
Marcus Bleicher, Strange Quark Matter 2006

26. Back up slides
Marcus Bleicher, Strange Quark Matter 2006

27. Model check: Expansion
Transverse Expansion of the bulk is described
Model uncertainties on level of 30-50%
Bratkovskaya, M.B. et al., Phys.Rev.C69:054907,2004
Uncertainties depend on: PYTHIA implementation and properties of high mass resonances
Marcus Bleicher, Strange Quark Matter 2006

28. Marcus Bleicher, Strange Quark Matter 2006